The invention relates to the field of holographic data storage, and more generally, to the problem of correcting errors that arise from the misregistration of detectors (e.g., pixels) and coherent beams of optical radiation.
The ever increasing demand for readily accessible information has been enabled by the increasing data storage capacity of computers and the decreasing cost of storing this data. Magnetic storage media have played a prominent role in the Information Age, and more recently, optical data storage technologies have become commonplace. However, both magnetic and conventional optical data storage technologies, in which individual bits are stored as distinct markers on the surface of the recording medium, are approaching physical limits beyond which the storage of even more information is impractical. Storing information throughout the volume of a medium, rather than just on its surface, appears to be a high capacity alternative to currently used information storage technologies. Holographic data storage is one such volumetric approach to data storage.
As shown in FIG. 1, with holographic data storage, an entire xe2x80x9cpagexe2x80x9d of information in the form of bit images is recorded at one time as an optical interference pattern within a holographic storage medium 10. Lithium niobate is one photosensitive optical material commonly used in holographic storage applications. The input data to be stored in the medium 10 is optically prepared by passing an input beam 14 of that light (e.g., from a laser, not shown) through a spatial light modulator (SLM) 18. The SLM 18 functions as a xe2x80x9cpixelatedxe2x80x9d input device and typically includes a liquid crystal panel similar to those used in laptop computers. Individual pixel elements 22 within the SLM 18 may be turned on or off (although shades of gray are also possible), as illustrated in FIG. 1 by the SLM""s white and dark elements, respectively. In this manner, the input beam 14 is spatially modulated to form an object beam 26 containing a page of information determined by the particular on/off configuration of the pixel elements 22 of the SLM 18; the object beam 26 may be thought of as containing an array of individual beams (not shown in FIG. 1) corresponding to SLM pixel elements 22. This information-containing object beam 26 may then be directed through one or more optical elements 30 such as a lens and into the holographic storage medium 10. The information contained in the object beam 26 can be recorded in the storage medium 10 by intersecting the object beam with a second beam 34 of coherent light (e.g., from a laser, not shown) known as the reference beam. The reference beam 34, which is of the same wavelength as the object beam 26, is designed to be easy to reproduce, e.g., it may be simply a collimated beam having a planar wavefront. Intersecting the object beam 26 and the reference beam 34 in the storage medium 10 produces an optical interference pattern that results in chemical and/or physical changes in the medium itself, such as a change in absorption or refractive index, thereby producing a grating within the storage medium. This optical interference pattern, recorded as physical changes to the material within the storage medium 10, contains the information represented by the corresponding on/off (or gray level) configuration of the SLM pixel elements 22.
Information may be retrieved from the storage medium 10 as illustrated in FIG. 2. The reference beam 34 is directed into the storage medium 10 which has now been physically altered to contain a grating corresponding to the interference pattern generated by the intersection of the object beam 26 and the reference beam 34. When the storage medium 10 is illuminated in this manner, some of the reference beam 34 is diffracted by the grating such that a reconstructed object beam 38 emerges from the storage medium 10. This reconstructed object beam 38 contains the same information (and propagates in the same direction) as the object beam 26. The reconstructed object beam 38 may then be imaged through one or more optical elements 42 (e.g., lens) and onto a grid or array 44 of discrete detector elements 48 or pixels (e.g., an array of nominally square pixels in a charge coupled device or CCD), so that the page of information (or xe2x80x9cdata pagexe2x80x9d) originally modulated onto the object beam 26 by the SLM pixel elements 22 can be retrieved. Alternatively, information may be retrieved by illuminating the storage medium 10 with a reference beam (not shown) that is phase-conjugate to the reference beam 34 (see J. Ashley et al., xe2x80x9cHolographic data storagexe2x80x9d, IBM J. Res. Develop., vol. 44, no. 3, May 2000, pp. 341-368). This phase conjugate reference beam is diffracted by the grating within the storage medium 10 to construct a phase-conjugate object beam. A beamsplitter and a polarization element maybe used to direct this phase-conjugate object beam onto the detector array 44. The relationship between a beam and its phase-conjugate is that they have exactly the same spatial wavefront, but propagate in opposite directions (much like a movie played in reverse).
A large number of interference gratings can be formed within a single storage medium 10 by altering the angle between the object beam 26 and the reference beam 34, or alternatively, by using other wavelengths for the object and reference beams. In this manner, a large number of data pages may be stored in the storage medium, and any particular data page can be read out independently of other data pages. The theoretical limit to this volumetric approach to data storage and retrieval has been estimated to be on the order of tens of terabits per cubic centimeter. (See J. Ashley et al., supra.) Holographic data storage also offers the prospect of faster access times, since laser beams can be moved rapidly (unlike actuators used in disk drives), and the output wavelength of certain kinds of lasers can be rapidly and accurately tuned.
To retrieve data from the storage medium 10 without error, the data page represented by the complex optical wavefront of the reconstructed object beam 38 would ideally be imaged onto the pixels 48 of the detector array 44 such that each of the individual beams (not shown in FIGS. 1 and 2) corresponding to an individual SLM pixel element 22 fell onto a single pixel 48 in the detector array 44. That is, the reconstructed optical beam 38 would be imaged onto the array 44 such that there would be a one-to-one correspondence between the SLM pixel elements 22 and the detector pixels 48. In practice, such a high degree of correlation is difficult to achieve. Misfocusing of the detector array 44 (e.g., with respect to the focal plane of the optical element 42) as well as optical aberrations in the imaging system lead to a situation in which energy that was intended for a particular pixel 48 lands on one or more adjacent pixels. This misregistration of the pixels 48 with the individual beams within the reconstructed object beam 38 results in interpixel interference or crosstalk. Interpixel interference may lead to errors in the retrieved data when signals from the pixels 48 are read out to, for example, a processor or computer (as in FIG. 3 below). However, in current holographic systems, some stressing of the physical components of the holographic system beyond the point of ideal imaging may be acceptable if coding and signal processing techniques can be employed to reduce the bit error rate (BER) to a sufficiently low level.
As discussed above, each portion of the data-bearing optical wavefront intended for an SLM pixel element 22 should ideally land on a single detector pixel 48. Both the SLM 18 and the output detector array 44 typically contain pixels on a nominally square grid having a grid-spacing or pitch xcex4. If the pixel pitches of the input and output devices are different, the optical imaging system is ideally designed to contain the appropriate magnification. However, the active area of the detector pixels 48 may be smaller than the pixels 48 themselves, giving rise to the xe2x80x9cfill factorxe2x80x9d of the pixel, measured either along the side of the pixel or as a fraction of the area used: active area/xcex42.
To maximize storage density, the holographic recording is done at a point where the data-bearing beam is tightly focussedxe2x80x94often an aperture is used to prevent other portions of the storage medium from being inadvertently exposed. The smaller this aperture, however, the more the resulting pixel images are blurred at the detector array 44. The optical system is characterized by a point spread function (PSF), which is the size of the (blurred) spot found at the output image plane when a point source is placed at the input plane (or alternatively, when a hologram of this same wavefront is reconstructed). Since the aperture is finite in size, the PSF will have periodic nulls or zeroes, and the spacing between these nulls will scale inversely with the limiting aperture at the medium. In principle, crosstalk between pixels could be entirely avoided by the combination of making each pixel very small in area followed by choosing an aperture such that the spacing between the peak and the first null of the PSF is identical to the pitch of the detector pixel 48. This aperture is termed the Nyquist aperture, and it is the smallest aperture for which sufficient information can be passed from the SLM 18 to the output array 44 to guarantee the reliable retrieval of information. This aperture may be defined by the dimensions of the storage medium 10 or by a component (not shown) positioned between the SLM 18 and the detector array 44. Unfortunately, the number of photons detected at the detector array 44 must be sufficient to overcome thermal noise at the detector array, and the benefits of a detector array arising from low-crosstalk are far outweighed by the loss of signal arising from the very small fill-factor. (See M-P. Bernal et al., xe2x80x9cBalancing interpixel cross talk and detector noise to optimize areal density in holographic storage systemsxe2x80x9d, Applied Optics, vol. 37, no. 23, pp. 5377-5385, 1998).
Linear signal processing techniques such as equalization, Wiener filtering, and partial-response-maximum-likelihood have had great success in deblurring the temporal 1-D channels found in conventional storage and communications systems. (See J. W. M. Bergmans, Digital baseband transmission and recording, Kluwer Academic Publishers, Boston, 1996.) This success led some investigators to propose signal processing schemes for page-oriented data storage that extend existing 1-D algorithms to 2-D but retain a simple linear channel model. (J. F. Heanue et al., xe2x80x9cSignal detection for page-access optical memories with intersymbol interferencexe2x80x9d, Applied Optics, vol. 35, no. 14, pp. 2431-2438, 1996; V. Vadde et al., xe2x80x9cChannel modeling and estimation for intrapage equalization in pixel-matched volume holographic data storagexe2x80x9d, Applied Optics, vol. 38, no. 20, Jul. 10, 1999; and B. M. King et al., xe2x80x9cParallel detection algorithm for page-oriented optical memoriesxe2x80x9d, Applied Optics, vol. 37, no. 26, Sep. 10, 1998.) Their reasoning was that by correcting the blur introduced by diffraction, it should be possible to work with smaller spatial apertures and thus higher areal densities.
However, the performance improvements achieved in holographic data storage systems using these techniques have been less dramatic than those achieved in 1-D systems. One reason for this is that the detection of the intensity of a coherent optical wavefront is an inherently nonlinear process, in which the electric fields (not the intensities) of two or more beams constructively or destructively interfere with each other. The resulting optical intensity at any given point is given by summing the electric fields from all the beams arriving at that point and squaring this sum. The intensity at each point of a pixel may depend (at least in part) on electric fields from signals that would have landed onto nearby pixels in the absence of misregistration. Each detector pixel integrates intensity over that pixel""s area to generate an output signal, in which the intensity at each point is given by summing the square of the total electromagnetic field at that point. Thus, in the absence of interference effects arising from coherent light, intensities from two or more different beams would simply add. With coherent light, however, deconvolving the intensity data from a pixel array to establish what the intensity data would have been in the absence of interference effects arising from misregistration is fundamentally a nonlinear process.
The problem of misregistration has typically been addressed through careful (but costly) engineering. The optical components between the SLM 18 and the detector array 44 can be configured to minimize optical distortion and magnification error, but simultaneously achieving high storage density and compact system size can be difficult. Alternatively, phase-conjugate readout can be used to reduce the impact of aberrations in most but not all of the optical system (F. Zhao et al., xe2x80x9cHigh density phase-conjugate holographic memory with phase-only image compressorsxe2x80x9d, Optical Memory and Neural Networks, vol. 6, no. 4, pp. 261-264, 1997). In either case, however, precise optomechanical mounting and some degree of lateral position feedback are necessary to achieve and maintain alignment. In practice, small data pages can almost be perfectly pixel-matched, i.e., the problem of misregistration can be, for all practical purposes, eliminated. However, with large megapixel or megapel (1024xc3x971024) data pages, a significant fraction of the signal-to-noise (SNR) budget can be consumed by even a small amount of optical distortion: In practice, one part of a data page must be slightly misaligned in order to bring another part of the data page into perfect alignment. Thus, there remains a need for a method of compensating for the errors resulting from the misregistration of a data page with an array of detector pixels.
One aspect of the invention is a processor-implemented method of determining the intensities of beams of coherent electromagnetic radiation, in which the beams form an array. The method comprises providing an array of detectors and imaging the array of beams onto the array of detectors to generate output signals from the detectors. The output signals are detected to record respective output signal levels, and the misregistration between the detectors and the beams is determined. A processor is used to correct the recorded output signal levels by compensating for electromagnetic interference effects at the detectors arising from the misregistration, so that the corrected output signals levels are proportional to those that would be recorded in the absence of misregistration. In a preferred implementation, the detector array is a two-dimensional array of pixels. The array may include at least (or exactly) 1024xc3x971024 pixels, or it may include at least (or exactly) 1024xc3x97768 pixels. In one preferred implementation, the coherent radiation includes laser light.
Determining the misregistration may advantageously include determining a set of static misregistrations between the detectors and the beams, determining any dynamic misalignment between the array of detectors and the array of beams, and then determining a set of total misregistrations between the detectors and the beams from the dynamic misregistration and the set of static misregistrations. In a preferred implementation, determining the dynamic misalignment between the array of detectors and the array of beams includes identifying the location of fiducial images on the detector array. The imaging of the array of beams preferably includes directing a beam of laser light through a holographic storage medium to reconstruct the array of beams. In one preferred implementation, compensating for electromagnetic interference effects includes determining, for each detector, the convolution of the optical point spread function (PSF) of beams in the array and the detector""s area. The compensating preferably includes performing iterative calculations in a first spatial dimension for detectors along a given row aligned along the first spatial dimension, and advantageously further includes performing iterative calculations in the first spatial dimension for detectors along additional rows aligned along the first spatial dimension. The compensating preferably further includes performing iterative calculations in a second spatial dimension for detectors along rows aligned with the second spatial dimension.
Another aspect of the invention is a processor-implemented method of correcting errors arising from interpixel cross talk in the detection of a reconstructed holographic data image, in which the data image includes a two dimensional grid of bit images arranged in rows and columns. The method includes providing a detection device having a grid of detector pixels, in which the detector pixels correspond to and detect the bit images. The data image is directed onto the detector pixels by passing coherent electromagnetic radiation through a holographic storage medium, and output signals are measured from the detector pixels. Any misregistration between the pixels and the bit images is determined, and a processor is used to correct the measured output signals to compensate for signal strength lost to or gained by nearby pixels through interference effects resulting from the misregistration, thereby producing a calculated data image that is substantially corrected for interpixel crosstalk. In a preferred implementation, the misregistration includes determining any dynamic misalignment between the image grid and the pixel grid, and determining any static misregistrations between the bit images and the pixels.
Correcting the measured output signals may advantageously include (a) for each pixel in a given row of pixels, adding to the output signal measured at that pixel any signal lost through interference effects to neighboring pixels in the given row, (b) for each pixel in the given row, subtracting from the output signal measured at that pixel any signal gained through interference effects from neighboring pixels in the given row, and (c) applying (a) and (b) to additional rows of pixels, thereby producing a data image of revised output signals. Correcting the measured output signals may further include (d) for each pixel in a given column of pixels, adding to the revised output signal for that pixel any signal lost through interference effects to neighboring pixels in the given column, (e) for each pixel in the given column, subtracting from the revised output signal for that pixel any signal gained through interference effects from neighboring pixels in the given column, and (f) applying (d) and (e) to additional columns of pixels. Analogous methods may be employed, in which columns are processed before rows.
A preferred implemenation includes iteratively processing the output signals from the detector pixels along a first dimension to produce an intermediate page of intensities, and processing the intermediate page intensities along a second dimension to produce the calculated data image. In one preferred implemenation, patterns of discrete bit images are imaged onto the detector pixels to determine the extent of the interference effects resulting from misregistrations between detector pixels and their respective bit images. In a preferred implementation, output signals are iteratively processed back and forth along each row to generate respective revised data signals, and output signals are iteratively processed back and forth along each column to generate respective revised data signals, in which only those revised data signals for which pixel offsets are less than or equal to one-half of the pixel spacing are retained. In another implementation, output signals are iteratively processed back and forth along each row to generate respective revised data signals, and output signals are iteratively processed back and forth along each column to generate respective revised data signals, in which, for at least some detector pixels, an average of the revised data signals is calculated. The method advantageously comprises including blank rows and columns in the data image to facilitate correcting of the measured output.